<!DOCTYPE html>

<html>

  <head>
    <title>Ch. 2 - Let's get you a robot</title>
    <meta name="Ch. 2 - Let's get you a robot" content="text/html; charset=utf-8;" />
    <link rel="canonical" href="http://manipulation.csail.mit.edu/robot.html" />

    <script src="https://hypothes.is/embed.js" async></script>
    <script type="text/javascript" src="chapters.js"></script>
    <script type="text/javascript" src="htmlbook/book.js"></script>

    <script src="htmlbook/mathjax-config.js" defer></script> 
    <script type="text/javascript" id="MathJax-script" defer
      src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js">
    </script>
    <script>window.MathJax || document.write('<script type="text/javascript" src="htmlbook/MathJax/es5/tex-chtml.js" defer><\/script>')</script>

    <link rel="stylesheet" href="htmlbook/highlight/styles/default.css">
    <script src="htmlbook/highlight/highlight.pack.js"></script> <!-- http://highlightjs.readthedocs.io/en/latest/css-classes-reference.html#language-names-and-aliases -->
    <script>hljs.initHighlightingOnLoad();</script>

    <link rel="stylesheet" type="text/css" href="htmlbook/book.css" />
  </head>

<body onload="loadChapter('manipulation');">

<div data-type="titlepage" pdf="no">
  <header>
    <h1><a href="index.html" style="text-decoration:none;">Robotic Manipulation</a></h1>
    <p data-type="subtitle">Perception, Planning, and Control</p> 
    <p style="font-size: 18px;"><a href="http://people.csail.mit.edu/russt/">Russ Tedrake</a></p>
    <p style="font-size: 14px; text-align: right;"> 
      &copy; Russ Tedrake, 2020-2023<br/>
      Last modified <span id="last_modified"></span>.</br>
      <script>
      var d = new Date(document.lastModified);
      document.getElementById("last_modified").innerHTML = d.getFullYear() + "-" + (d.getMonth()+1) + "-" + d.getDate();</script>
      <a href="misc.html">How to cite these notes, use annotations, and give feedback.</a><br/>
    </p>
  </header>
</div>

<p pdf="no"><b>Note:</b> These are working notes used for <a
href="http://manipulation.csail.mit.edu/Fall2023/">a course being taught
at MIT</a>. They will be updated throughout the Fall 2023 semester.  <!-- <a 
href="https://www.youtube.com/channel/UChfUOAhz7ynELF-s_1LPpWg">Lecture  videos are available on YouTube</a>.--></p> 

<table style="width:100%;" pdf="no"><tr style="width:100%">
  <td style="width:33%;text-align:left;"><a class="previous_chapter" href=intro.html>Previous Chapter</a></td>
  <td style="width:33%;text-align:center;"><a href=index.html>Table of contents</a></td>
  <td style="width:33%;text-align:right;"><a class="next_chapter" href=pick.html>Next Chapter</a></td>
</tr></table>

<script type="text/javascript">document.write(notebook_header('robot'))
</script>
<!-- EVERYTHING ABOVE THIS LINE IS OVERWRITTEN BY THE INSTALL SCRIPT -->
<chapter style="counter-reset: chapter 1"><h1>Let's get you a robot</h1>
      
  <p>In this chapter we're going to outfit your <a
  href="https://en.wikipedia.org/wiki/Mecha">mech</a>.  I want to make sure you
  understand the robot hardware that we're using in these notes, and how it
  compares to the other hardware available today.  You should also come away
  with an understanding of how we simulate the robot and what commands you
  can send to the robot interface.</p>
    
  <section><h1>Robot description files</h1>
  
    <p>In the majority of the chapters, we'll make repeated use of just one or
    two robot configurations. One of the great things about modern robotics is
    that many of the tools we will develop over the course of these notes are
    quite general, and can be transferred from one robot to another easily. I
    could imagine a future version of these notes where you really do get to
    build out your robot in this chapter, and use your customized robot for the
    remaining chapters!</p>
    
    <p>The ability to easily simulate/control a variety of robots is made
    possible in part by the proliferation of common file formats for describing
    our robots.  Unfortunately, the field has not converged on a single
    preferred format (yet), and each of them have their quirks. Drake currently
    loads <a href="http://wiki.ros.org/urdf">Universal Robot Description
    Format</a> (URDF), <a href="http://sdformat.org/">Simulation Description
    Format</a> (SDF), and has limited support for the <a
    href="https://mujoco.readthedocs.io/en/latest/XMLreference.html">MuJoCo
    format</a> (MJCF). The Drake developers have been trying to upstream
    improvements to SDF rather than start yet another format, but we do have a
    very simple YAML specification called <a
    href="https://drake.mit.edu/doxygen_cxx/structdrake_1_1multibody_1_1parsing_1_1_model_directives.html">Drake
    Model Directives</a> which makes it very quick and easy to load multiple
    robots/objects from these different file formats into one simulation; you
    saw an example of this in the
    <script>document.write(notebook_link('intro', deepnote, "introduction chapter notebook"))</script>.</p>

  </section>

  <section><h1>Arms</h1>

    <p>There appear to be a lot of robotics arms available on the market.  So
    how does one choose?  Cost, reliability, usability, payload, range of
    motion, ...; there are many important considerations.  And the choices we
    might make for a research lab might be very different than the choices we
    might make as a startup.</p>
    
    <example><h1>Robot arms</h1>
    
      <p>I've put together a simple example to let you explore some of the
      various robot arms that are popular today. Let me know if your favorite arm isn't on the list yet!</p>
      
      <script>document.write(notebook_link('robot', d=deepnote, link_text="", notebook='inspector'))</script>

    </example>

    <p>There is one particular requirement which, if we want our robot to
    satisfy, quickly winnows the field to only a few viable platforms: that
    requirement is joint-torque sensing and control.  Out of the
    torque-controlled robots on the market, I've used the Kuka LBR iiwa robot
    most often throughout these notes (I will try to use the lower case "iiwa"
    to be <a
    href="https://www.kuka.com/en-us/products/robotics-systems/industrial-robots/lbr-iiwa">consistent
    with the manufacturer</a>, but it looks wrong to me every time!).  </p>
    
    <figure>
      <img width="60%" src="https://www.robots.com/images/robots/KUKA/Collaborative/KUKA_LBR_IIWA_7_0001.png"/>
      <figcaption><a href="https://www.kuka.com/en-us/products/robotics-systems/industrial-robots/lbr-iiwa">Kuka LBR iiwa robot</a>.  This one has a 7kg payload.</figcaption>
    </figure>

    <p>It's not absolutely clear that the joint-torque sensing and control
    feature is required, even for very advanced applications, but as a
    researcher who cares a great deal about the contact interactions between my
    robots and the world, I prefer to have the capability and explore whether I
    need it rather than wonder what life might have been like. To better
    understand why, let us start by understanding the difference between most
    robots, which are position-controlled, and the handful of robots that have
    accepted the additional cost and complexity to provide torque sensing and
    control.</p>
    
    <subsection id="position-controlled"><h1>Position-controlled robots</h1>

      <figure>
        <img height="200px" src="https://www.robots.com/images/robots/Universal/Universal_UR10_0002.jpg" />
        <img height="200px" src="https://webshop.robotics.abb.com/media/catalog/product/d/u/dual_arm_yumi_14000_main.jpg" />
        <figcaption>Two popular position controlled manipulators.  (Left) The UR10 from Universal Robotics. (Right) The ABB Yumi.</figcaption>
      </figure>

      <p>Most robot arms today are "position controlled" -- given a desired
      joint position (or joint trajectory), the robot executes it with
      relatively high precision.  Basically all arms can be position controlled
      -- if the robot offers a torque control interface (with sufficiently high
      bandwidth) then we can certainly regulate positions, too.  In practice,
      calling a robot "position controlled" is a polite way of saying that it
      does not offer torque control.  Do you know why position control and not
      torque control is the norm?</p>

      <p>Lightweight arms like the examples above are actuated with electric
      motors.  For a reasonably high-quality electric motor (with windings
      designed to minimize torque ripple, etc), we expect the torque that the
      motor outputs to be directly proportional to the current that we apply:
      $$\tau_{motor} = k_t i,$$ where $\tau_{motor}$ is the motor torque, $i$ is
      the applied current, and $k_t$ is the "<a
      href="https://en.wikipedia.org/wiki/Motor_constants">motor torque
      constant</a>". (Similarly, applied voltage has a simple (affine)
      relationship with the motor's steady-state velocity).  If we can control
      the current, then why can we not control the torque?  
      </p>

      <p>The short answer is that to achieve reasonable cost and weight, we
      typically choose small electric motors with large gear reductions, and
      gear reductions come with a number of dynamic effects that are very
      difficult to model -- including backlash, vibration, and friction. So the
      simple relationship between current and torque breaks down.  Conventional
      wisdom is that for large gear ratios (say $\gg 10$), the unmodeled terms
      are significant enough that they cannot be ignored, and torque is no
      longer simply related to current.</p>

      <subsubsection><h1>Position Control.</h1>

        <p>How can we overcome this challenge of not having a good model of the
        transmission dynamics?  Regulating the current or speed <i>of the
        motor</i> only requires sensors on the motor side of the transmission.
        To accurately regulate the joint, we typically need to add more sensors
        on the output side of the transmission. Importantly, although the
        torques due to the transmission are not known precisely, they are also
        not arbitrary -- for instance they will never add energy into the
        system. Most importantly, we can be confident that there is a
        <i>monotonically increasing</i> relationship between the current that
        we put into the motor and the torque at the joint, and ultimately the
        acceleration of the joint.  Note that I chose the term monotonic
        carefully, meaning "non-decreasing" but <i>not</i>
        implying "strictly increasing", because, for instance, when a joint is
        starting from rest, static friction will resist small torques without
        having any acceleration at the output.</p>

        <p>The most common sensor to add to the joint is a position sensor --
        typically an encoder or potentiometer -- these are inexpensive,
        accurate, and robust.  In practice, we think of these as providing
        (after some signal filtering/conditioning) accurate measurements of the
        joint position and joint velocity -- joint accelerations can also be
        obtained via differentiating twice but are generally considered more
        noisy and less suitable for use in tight feedback loops.  Position
        sensors are sufficient for accurately tracking desired position
        trajectories of the arm.  For each joint, if we denote the joint
        position as $q$ and we are given a desired trajectory $q^d(t)$, then I
        can track this using <a
        href="https://en.wikipedia.org/wiki/PID_controller">proportional-integral-derivative
        (PID) control</a>: $$\tau = k_p (q^d - q) + k_d (\dot{q}^d - \dot{q}) +
        k_i \int (q^d - q) dt,$$ with $k_p$, $k_d$, and $k_i$ being the
        position, velocity, and integral gains.  PID control has a rich theory,
        and a trove of knowledge about how to choose the gains, which I will
        not reproduce here.  I will note, however, that when we simulate
        position-controlled robots we often need to use different gains for the
        physical robot and for our simulations. This is due to the transmission
        dynamics, but also the fact that PID controllers in hardware typically
        output voltage commands (via <a
        href="https://en.wikipedia.org/wiki/Pulse-width_modulation">pulse-width
        modulation</a>) instead of current commands. Closing this modeling gap
        has traditionally not been a priority for robot simulation -- there are
        enough other details to get right which dominate the "sim-to-real" gap
        -- but I suspect that as the field matures the mainstream robotics
        simulators will eventually capture this, too.</p>
        
        <p>Some of you are thinking, "I can train a neural network to model
        <i>anything</i>, I'm not afraid of difficult-to-model transmissions!" I
        do think there is reason to be optimistic about this approach; there
        are a number of initial demonstrations in this direction (e.g.
        <elib>Hwangbo19</elib>). This is not quite as useful as if we can have
        a first-principles model that can generalize to new actuators from a
        few parameters in a description file, but could be very productive.</p>

        <todo>Think through the implications of the PWM voltage command instead
        of direct motor current.</todo>

        <todo>Add a simulation of a single joint against gravity with PID
        control gains on sliders, following a sinusoidal trajectory.</todo>

      </subsubsection>

      <subsubsection><h1>An aside: link dynamics with a transmission.</h1>

        <p>One thing that might be surprising is that, despite the fact that
        the joint dynamics of a manipulator are highly coupled and state
        dependent, the PID gains are often chosen independently for each joint,
        and are constant (not <a
        href="https://en.wikipedia.org/wiki/Gain_scheduling">gain-scheduled</a>
        ). Wouldn't you expect for the motor commands required for e.g. a robot
        arm at full extension holding a milk jug might be very different than
        the motor commands required when it is unloaded in a vertical hanging
        position? Surprisingly, the required gains/commands might not be as
        different as one would think.</p>
          
        <p>Electric motors are most efficient at high speeds (often > 100 or
        1,000 rotations per minute).  We probably don't actually want our robots
        to move that fast even if they could!  So nearly all electric robots
        have fairly substantial gear reductions, often on the order of 100:1;
        the transmission output turns one revolution for every 100 rotations of
        the motor, and the output torque is 100 times greater than the motor
        torque.  For a gear ratio, $n$, actuating a joint $q$, we have
        $$q_{motor} = n q,\quad \dot{q}_{motor} = n \dot{q}, \quad
        \ddot{q}_{motor} = n \ddot{q}, \qquad \tau_{motor} = \frac{1}{n} \tau.$$
        Interestingly, this has a fairly profound impact on the resulting
        dynamics (given by $f = ma$), even for a single joint.  Writing the
        relationship between joint torque and joint acceleration (no motors
        yet), we can write $ma = \sum f$ in the rotational coordinates as
        $$I_{arm} \ddot{q} = \tau_{gravity} + \tau,$$ where $I_{arm}$ is the
        moment of inertia. For example, for a <a
        href="http://underactuated.mit.edu/pend.html"
        target="underactuated">simple pendulum</a>, we might have $$ml^2
        \ddot{q} = - mgl\sin{q} + \tau.$$  But the applied joint torque $\tau$
        actually comes from the motor -- if we write this equation in terms of
        motor coordinates we get: $$\frac{I_{arm}}{n} \ddot{q}_{motor} =
        \tau_{gravity} + n\tau_{motor}.$$  If we divide through by $n$, and take
        into account the fact that the motor itself has inertia (e.g. from the
        large spinning magnets) that is not affected by the gear ratio, then we
        obtain: $$\left(I_{motor} + \frac{I_{arm}}{n^2}\right) \ddot{q}_{motor}
        = \frac{\tau_{gravity}}{n} + \tau_{motor}.$$</p>
          
        <p>It's interesting to note that, even though the mass of the motors
        might make up only a small fraction of the total mass of the robot, for
        highly geared robots they can play a significant role in the dynamics
        of the joints. We use the term <i>reflected inertia</i> to denote the
        inertial load that is felt on the opposite side of a transmission, due
        to the scaling effect of the transmission. The "reflected inertia" of
        the arm at the motor is cut by the square of the gear ratio; or the
        "reflected inertia" of the motor at the arm is multiplied by the square
        of the gear ratio.  This has interesting consequences -- as we move to
        the multi-link case, we will see that $I_{arm}$ is a <a
        href="http://underactuated.mit.edu/multibody.html"
        target="underactuated">state-dependent function that captures the
        inertia of the actuated link and also the inertial coupling of the
        other joints in the manipulator</a>. $I_{motor}$, on the other hand, is
        constant and only affects the local joint. For large gear ratios, the
        $I_{motor}$ terms dominate the other terms, which has two important
        effects: 1) it effectively diagonalizes the manipulator equations (the
        inertial coupling terms are relatively small), and 2) the dynamics are
        relatively constant throughout the workspace (the state-dependent terms
        are relatively small). These effects make it relatively easy to tune
        constant feedback gains for each joint individually that perform well
        in all configurations.</p>

        <todo>The WSG is a great example of reflected inertia!</todo>
      </subsubsection>

    </subsection>

    <subsection><h1>Torque-controlled robots</h1>

      <p>Although not as common, there are a number of robots that do support
      direct control of the joint torques.  There are a handful of ways that
      this capability can be realized.</p>  
        
      <p>It <i>is</i> possible to actuate a robot using electric motors that
      require only a small gear reduction (e.g. $\le$ 10:1) where the frictional
      forces are negligible.  In the past, these "direct-drive
      robots"<elib>Asada87</elib> had enormous motors and limited payloads.
      More recently, robots like the <a
      href="https://robots.ieee.org/robots/wam/">Barrett WAM</a> arm used cable
      drives to keep the arm light by having large motors in the base.  And
      just in the last few years, we've seen progress in high-torque outrunner
      and frameless motors bringing in a new generation of low-cost,
      "quasi-direct-drive" robots: e.g. MIT Cheetah <elib>Wensing17</elib>, <a
      href="http://rll.berkeley.edu/blue/">Berkeley Blue</a>, and <a
      href="https://www.halodi.com/">Halodi Eve</a>.</p>

      <p>Hydraulic actuators provide another solution for generating large
      torques without large transmissions.  Sarcos had a series of <a
      href="https://www.youtube.com/watch?v=VDxWHNtZvyI">torque-controlled
      arms</a> (and humanoids), and many of the most famous robots from <a
      href="https://www.bostondynamics.com/robots">Boston Dynamics</a> are based
      on hydraulics (though there is an increasing trend towards electric
      motors).  These robots typically have a single central pump and each
      actuator has a (lightweight) valve that can shunt fluid through the
      actuator or through a bypass; the differential pressure across the
      actuator is at least approximately related to the resulting
      force/torque.</p>

      <p>Another approach to torque control is to keep the large gear-ratio
      motors, but add sensors to directly measure the torque at the joint side
      of the actuator.  This is the approach used by the Kuka iiwa robot that we
      use in the example throughout this text; the iiwa actuators have <a
      href="https://en.wikipedia.org/wiki/Strain_gauge">strain gauges</a>
      integrated into the transmission.  However there is a trade-off between
      the stiffness of the transmission and the accuracy of the force/torque
      measurement <elib>Kashiri17</elib> -- the iiwa transmission includes an
      explicit "Flex Spline" with a stiffness around 5000 Nm/rad
      <elib>Wedler12</elib>.  Taking this idea to an extreme, Gill Pratt
      proposed "series-elastic actuators" that have even lower stiffness springs
      in the transmission, and proposed measuring joint position on both the
      motor and joint sides of the transmission to estimate the applied torques
      <elib>Pratt95b</elib>.  For example, the <a
      href="https://en.wikipedia.org/wiki/Baxter_(robot)">Baxter</a> and Sawyer
      robots from Rethink used series-elastic actuators; I don't think they
      ever published the spring stiffness values but similarly-motivated
      series-elastic actuators from <a
      href=http://docs.hebi.us/hardware.html>HEBI robotics are closer to 100
      Nm/rad</a>.  Even for the iiwa actuators, the joint elasticity is
      significant enough that the low-level controllers go to great length to
      take it into account explicitly in order to achieve high-performance
      control of the joints<elib>Albu-Schaffer07</elib>.  We will discuss these
      details when we get to the chapter covering <a href="force.html">force
      control</a>.</p>

    </subsection>
    
    <subsection><h1>A proliferation of hardware</h1>
    
      <p>The low-cost torque-controlled arms that I mentioned above are just
      the beginnings in what promises to be a massive proliferation of robotic
      arms. During the pandemic, I saw a number of people using inexpensive
      robots like the <a
      href="https://www.ufactory.cc/xarm-collaborative-robot">xArm</a>
      at home. As demand increases, costs will continue to come down.</p>
      
      <p>Let me just say that, compared to working on legged robots, where for
      decades we did our research on laboratory prototypes built by graduate
      students (and occasionally professors!) in the machine shop down the hall,
      the availability of professionally engineered, high-quality, high-uptime
      hardware is an absolute treat.  This also means that we can test
      algorithms in one lab and have another lab perhaps at another university
      testing algorithms on almost identical hardware; this facilitates levels
      of repeatability and sharing that were impossible before. The fact that
      the prices are coming down, which will mean many more similar robots in
      many more labs/environments, is one of the big reasons why I am so
      optimistic about the next few years in the field.</p>
      
      <p>It's a good time to be working on manipulation!</p>
      
    </subsection>
    
    <subsection><h1>Simulating the Kuka iiwa</h1>
    
      <p>It's time to simulate our chosen robotic arm.  The first step is to
      obtain a robot description file (typically URDF or SDF). For convenience,
      we <a
      href="https://github.com/RobotLocomotion/drake/tree/master/manipulation/models">ship</a>
      the models for a few robots, including iiwa, with Drake.  If you're
      interested in simulating a different robot, you can find either a URDF or
      SDF describing most commercial robots somewhere online.  But a word of
      warning: the quality of these models can vary wildly.  We've seen
      surprising errors in even the kinematics (link lengths, geometries, etc),
      but the dynamics properties (inertia, friction, etc) in particular are
      often not accurate at all. Sometimes they are not even mathematically
      consistent (e.g. it is possible to specify an inertial matrix in URDF/SDF
      which is not physically realizable by any rigid body).  Drake will
      complain if you ask it to load a file with this sort of violation; we
      would rather alert you early than start generating bogus simulations.
      There is also increasingly good support for exporting to a robot format
      directly from CAD software like <a
      href="http://wiki.ros.org/sw_urdf_exporter">Solidworks</a>.</p>
      
      <p>Now we have to import this robot description file into our physics
      engine.  In Drake, the physics engine is called
      <code>MultibodyPlant</code>.  The term "plant" may seem odd but it is
      pervasive; it is the word used in the controls literature to represent a
      physical system to be controlled, which originated in the control of
      chemical plants. This connection to control theory is very important to
      me. Not many physics engines in the world go to the lengths that Drake
      does to make the physics engine compatible with control-theoretic design
      and analysis.</p>
      
      <p>The <a
      href="https://drake.mit.edu/doxygen_cxx/classdrake_1_1multibody_1_1_multibody_plant.html"><code>MultibodyPlant</code></a>
      has a class interface with a rich library of methods to work with the
      kinematics and dynamics of the robot. If you need to compute the location
      of the center of mass, or a kinematic Jacobian, or any similar queries,
      then you'll be using this class interface. A 
      <code>MultibodyPlant</code> also implements the interface to be used as a
      <code>System</code>, with input and output ports, in Drake's <a
      href="https://medium.com/toyotaresearch/drake-model-based-design-in-the-age-of-robotics-and-machine-learning-59938c985515">systems
      framework</a>. In order to simulate, or analyze, the combination of a
      <code>MulitbodyPlant</code> with other systems like our perception, planning, and
      control systems, we will be assembling <a
      href="https://en.wikibooks.org/wiki/Control_Systems/Block_Diagrams">block
      diagrams</a>.</p>
      
      <div>
        <script src="htmlbook/js-yaml.min.js"></script>
        <script type="text/javascript">
        var sys = jsyaml.load(`
name: MultibodyPlant
input_ports:
- applied_generalized_force
- applied_spatial_force
- <em style="color:gray">model_instance_name[i]</em>_actuation
- <span style="color:green">geometry_query</span>
output_ports:
- continuous_state
- body_poses
- body_spatial_velocities
- body_spatial_accelerations
- generalized_acceleration
- reaction_forces
- contact_results
- <em style="color:gray">model_instance_name[i]</em>_continuous_state
- '<em style="color:gray">
  model_instance_name[i]</em>_generalized_acceleration'
- '<em style="color:gray">
  model_instance_name[i]</em>_generalized_contact_forces'
- <span style="color:green">geometry_pose</span>`);
        document.write(system_html(sys, "https://drake.mit.edu/doxygen_cxx/classdrake_1_1multibody_1_1_multibody_plant.html"));
        </script>
      </div> 
      
      <p>As you might expect for something as complex and general as a physics
      engine, it has many input and output ports; most of them are optional.
      I'll illustrate the mechanics of using these in the following example.</p>
      
      <example><h1>Simulating the passive iiwa</h1>
      
        <p>It's worth spending a few minutes with this example, which should
        help you understand not only the physics engine, but some of the basic
        mechanics of working with simulations in Drake.</p>

        <script>document.write(notebook_link('robot', d=deepnote, link_text="",notebook='simulation'))</script>
    
      </example>
      
      <p>The best way to visualize the results of a physics engine is with a 2D
      or 3D visualizer.  For that, we need to add the system which curates the
      geometry of a scene; in Drake we call it the <code>SceneGraph</code>.
      Once we have a <code>SceneGraph</code>, then there are a number of
      different visualizers and sensors that we can add to the system to
      actually render the scene.</p>
      
      <div>
        <script type="text/javascript">
        var sys = jsyaml.load(`
name: SceneGraph
input_ports:
- source_pose{0}
- ...
- source_pose{N-1}
output_ports:
- lcm_visualization
- query`);
        document.write(system_html(sys, "https://drake.mit.edu/doxygen_cxx/classdrake_1_1geometry_1_1_scene_graph.html"));
        </script>
      </div>       
      
      <example><h1>Visualizing the scene</h1>
      
        <p>This example is far more interesting to watch.  Now we have the 3D visualization!</p>

        <script>document.write(notebook_link('robot', d=deepnote, link_text="",notebook='simulation'))</script>

      </example>
      
      <p>You might wonder why <code>MultibodyPlant</code> doesn't handle the
      geometry of the scene as well.  Well, there are many applications in
      which we'd like to render complex scenes, and use complex sensors, but
      supply custom dynamics instead of using the default physics engine.
      Autonomous driving is a great example; in that case we want to populate a
      <code>SceneGraph</code> with all of the geometry of the vehicles and
      environment, but we often want to simulate the vehicles with very simple
      vehicle models that stop well short of adding tire mechanics into our
      physics engine. We also have a number of examples of this workflow in my
      <a href="http://underactuated.mit.edu">Underactuated Robotics</a> course,
      where we make extensive use of "simple models".</p>
      
      <p>We now have a basic simulation of the iiwa, but already some subtleties
      emerge.  The physics engine needs to be told what torques to apply at the
      joints.  In our example, we apply zero torque, and the robot falls down.
      In reality, that never happens; in fact there is essentially never a
      situation where the physical iiwa robot experiences zero torque at the
      joints, even when the controller is turned off.  Like many mature
      industrial robot arms, iiwa has mechanical brakes at each joint that are
      engaged whenever the controller is turned off.  To simulate the robot with
      the controller turned off, we would need to tell our physics engine about
      the torques produced by these brakes.</p>
      
      <p>In fact, even when the controller is turned on, and despite the fact
      that it is a torque-controlled robot, we can never actually send zero
      torques to the motors.  The iiwa software interface accepts "feed-forward
      torque" commands, but it will always add these as additional torques to
      its low-level controller which is compensating for gravity and the
      motor/transmission mechanics.  This often feels frustrating, but probably
      we don't actually want to get into the details of simulating the drive
      mechanics.</p>
      
      <p>As a result, the simplest reasonable simulation we can provide of the
      iiwa must include a simulation of Kuka's low-level controller.  We will
      use the iiwa's "joint impedance control" mode, and will describe the
      details of that once they become important for getting the robot to
      perform better.  For now, we can treat it as given, and produce our
      simplest reasonable iiwa simulation.</p>
      
      <example><h1>Adding the iiwa low-level controller</h1>

        <p>This example adds the iiwa controller and sets the desired <i>positions</i> (no longer the desired torques) to be the current state of the robot.  It's a more faithful simulation of the real robot.  I'm sorry that it is boring once again!</p>

        <script>document.write(notebook_link('robot', d=deepnote, link_text="",notebook='simulation'))</script>
        
      </example>

      <p>As a final note, you might think that simulating the <i>dynamics</i> of
      the robot is overkill, if our only goal is to simulate manipulation tasks
      where the robot is moving only relatively slowly, and effects of mass,
      inertia and forces might be less important than just the positions that
      the robot (and the objects) occupy in space.  I would actually agree with
      you.  But it's surprisingly tricky to get a <i>kinematic</i> simulation to
      respect the basic rules of interaction; e.g. to know when the object gets
      picked up or when it does not (see, for instance <elib>Pang18</elib>).
      Currently, in Drake, we mostly use the full physics engine for simulation,
      but often use simpler models for manipulation planning and control.</p>
      
    </subsection>

  </section>

  <section><h1>Hands</h1>
    
    <p>You might have noticed that the iiwa model does not actually have a hand
    attached; the robot ships with a mounting plate so that you can attach the
    "end-effector" of your choice (and some options on access ports so you can
    connect your end-effector to the computer without wires running down the
    outside of the robot).  So now we have another decision to make: what hand
    should we use?</p>
    
    <example><h1>Robot hands</h1>
    
      <p>We can explore different hand models in Drake using the same sort of
      interface we used for the arms, though I don't have as many hand models
      here yet.  Let me know if your favorite hand isn't on the list!</p>
      
      <script>document.write(notebook_link('robot', d=deepnote, link_text="",notebook='inspector'))</script>

    </example>    

    <p>It is interesting that, when it comes to robot end effectors, researchers
    in manipulation tend to partition themselves into a few distinct camps.</p>
    
    <subsection><h1>Dexterous hands</h1>
    
      <figure>
        <table><tr><td>
        <img style="height:250px" src="figures/shadow_dexterous_hand.jpg"/>
        </td><td style="width:50px"></td><td>
        <img style="height:250px" src="figures/allegro_hand.png"/>
        </td></tr>
        </table>
        <figcaption>Dexterous hands.  Left: the <a href="https://www.shadowrobot.com/products/dexterous-hand/">Shadow Dexterous Hand</a>.  Right: the <a href="http://www.wonikrobotics.com/Allegro-Hand.htm">Allegro Hand</a>.</figcaption>
      </figure>

      <p>Of course, our fascination with the human hand is well placed, and we
      dream of building robotic hands that are as dexterous and sensor-rich.
      But the reality is that we aren't there yet.  Some people choose to pursue
      this dream and work with the best dexterous hands on the market, and
      struggle with the complexity and lack of robustness that ensues.  The famous <a href="https://openai.com/blog/learning-dexterity/">"learning dexterity"</a> project from OpenAI used the Shadow hand for playing with a Rubik's cube, and the work that had to go into the hand in order to support the endurance learning experiments was definitely a part of the story.  There is a chance that new manufacturing techniques could really disrupt this space -- videos like <a href="https://www.youtube.com/watch?v=cZuzXdMyJsA">this one of FLLEX v2</a> look amazing<elib>Kim19</elib> -- and I am very optimistic that we'll have more capable and robust dexterous hands in the not-so-distant future.</p>
      
    </subsection>

    <subsection><h1>Simple grippers</h1>
    
      <figure>
        <iframe width="420" height="330" src="https://www.youtube.com/embed/oyHWkQcin7I" frameborder="0" allow="accelerometer; encrypted-media; gyroscope; picture-in-picture" allowfullscreen pdf="no"></iframe>
        <p pdf="only"><a href="https://www.youtube.com/embed/oyHWkQcin7I">Click here to watch the video.</a></p>
        <figcaption>This video of tele-operation with the PR1 from Ken
        Salisbury's group is now a classic example of doing amazingly useful
        things with a very simple hand.  Check out their <a
        href="https://sr.stanford.edu/?page_id=509">website</a> for more
        videos, including sweeping, fetching a beer, and unloading a
        dishwasher.</figcaption>
      </figure>

      <p><img style="width:150px;float:right;margin-left:10px"
      src="figures/toy_robot_hand.jpg"/>Another camp points out that dexterous
      hands are not necessary -- I can give you a simple gripper from the toy
      store and you can still accomplish amazingly useful tasks around the home.
      The PR1 videos above are a great demonstration of this.</p>

      <p>Another important argument in favor of simple hands is the elegance
      and clarity that comes from reducing the complexity.  If thinking clearly
      about simple grippers helps us understand more deeply <i>why</i> we need
      more dexterous hands (I think it will), then great.  For most of these
      notes, a simple two-fingered gripper will serve our pedagogical goals the
      best.  In particular, I've selected the Schunk WSG 050, which we have
      used extensively in our research over the last few years.  We'll also
      explore a few different end-effectors in later chapters, when they help
      to explain the concepts.</p>
  
      <p>To be clear: just because a hand is simple (few degrees of freedom)
      does not mean that it is low quality.  On the contrary, the Schunk WSG is
      a very high-quality gripper with force control and force measurement at
      its single degree of freedom that surpasses the fidelity of the Kuka.  It
      would be hard to achieve the same in a dexterous hand with many
      joints.</p>

    </subsection>

    <subsection><h1>Soft/underactuated hands</h1></subsection>

      <p>Finally, the third and newest camp is promoting clever mechanical
      designs for hands, which are often called "underactuated hands". The
      basic idea is that, for many tasks, you might not need as many actuators
      in your hand as you have joints. Many underactuated hands use a
      cable-drive mechanism to close the fingers, where a single tendon can
      cause multiple joints in the finger to bend. When designed correctly,
      these mechanisms can allow the finger to <a
      href="https://www.youtube.com/watch?v=C340gbK3sZc">conform passively to
      the shape of an object being grasped</a> with no change in the actuator
      command (c.f. <elib>Odhner14</elib>).  Cables are not required for this
      concept to work; qualitatively similar behavoir can be achieved using
      clever rigid mechanical linkages, as well.</p>
      
      <figure>
        <table><tr><td>
        <img style="height:250px" src="figures/RHR_Reflex_s.png"/>
        </td><td style="width:50px"></td><td>
        <img style="height:250px" src="figures/robotiq-3-finger-gripper.jpeg"/>
        </td></tr>
        </table>
        <figcaption>Underactuated hands.  Left: the RightHand Robotics Reflex2 is a descendant of the i-HY hand<elib>Odhner14</elib>.  Right: the Robotiq 3-fingered gripper.</figcaption>
      </figure>
      
      <figure>
        <img width="560" src="figures/robotiq_3_finger_mechanism.jpeg">
        <figcaption>A <a
          href="https://blog.robotiq.com/3-finger-adaptive-gripper-simulation-data">clever mechanical linkage</a> allows the underactuated Robotiq 3-fingered gripper to comply to an object being grasped.</figcaption>
      </figure>

      <p>Taking the idea of underactuation and passive compliance to an
      extreme, recent years have also seen a number of hands (or at least
      fingers) that are completely soft. The "soft robotics community" is
      rapidly changing the state of the art in terms of robot fabrication, with
      appendages, actuators, sensors, and even power sources that can be
      completely soft. These technologies promise to improve durability,
      decrease cost, and potentially be more safe for operating around
      people.</p>

      <figure>
        <table><tr><td>
          <img style="width:250px" src="figures/truby_soft_hand.jpeg"/>
        </td><td style="width:50px"></td><td>
          <img style="height:200px" src="figures/rbohand_disney.png"/>
        </td></tr>
        </table>
        <figcaption>Underactuated hands.  Left: A <a href="https://doi.org/10.1038/d41586-018-02778-5">3D-printed soft hand from Harvard</a> (Image credit: Ryan Truby).  Right: The <a href="http://www.robotics.tu-berlin.de/menue/research/soft_hands/">RBO Hand 2</a> (Image credit: Disney Research Zurich).</figcaption>
      </figure>

      <p>Underactuated hands can be excellent examples of mechanical design
      reducing the burden on the actuators / control system. Often these hands
      are amazingly good at some range of tasks (most often "enveloping
      grasps"), but not as general purpose.  It would be very hard to use one
      of these to, for instance, button my shirt. They are, however, becoming more and more dexterous; check out the video below!</p>

      <figure>
        <iframe width="560" height="315" src="https://www.youtube.com/embed/Z6ECG3KHibI" frameborder="0"
          allow="accelerometer; encrypted-media; gyroscope; picture-in-picture" allowfullscreen pdf="no"></iframe>
          <p pdf="only"><a href="https://www.youtube.com/embed/Z6ECG3KHibI">Click here to watch the video.</a></p>
        </figure>
  

    <subsection><h1>Other end effectors</h1>
    
      <p>Not all end effectors need to operate like dexterous or simplified
      human hands. Many industrial applications these days are doing a form of
      pick and place manipulation using vacuum grippers (also known as
      suction-cup grippers). Suction cups work extremely well on many but not all objects. Some objects are too soft or porous to be suctioned effectively. Some objects are too fragile or heavy to be lifted from a vacuum at the top of the object, and must be supported from below. Some hands have suction in the palms to achieve an initial pick, but still use more traditional fingers to stabilize a grasp.</p>

      <p>There are numerous other clever gripper technologies. One of my
      favorites is the <a
      href="https://www.creativemachineslab.com/jamming-gripper.html">jamming
      gripper</a>.  These grippers are made of a balloon filled with coffee
      grounds, or some other granular media; pushing down the balloon around an
      object allows the granular media to flow around the object, but then
      applying a vacuum to the balloon causes the granular media to "jam",
      quickly hardening around the object to make a stable grasp
      <elib>Brown10</elib>. </p>

      <figure>
        <iframe width="420" height="315" src="https://www.youtube.com/embed/bFW7VQpY-Ik" frameborder="0"
          allow="accelerometer; encrypted-media; gyroscope; picture-in-picture" allowfullscreen pdf="no"></iframe>
          <p pdf="only"><a href="https://www.youtube.com/embed/-KxjVlaLBmk">Click here to watch the video.</a></p>
      </figure>
  
      <p><a href="https://www.youtube.com/watch?v=r_HaJfANyT8">Here</a> is another clever design with actuated rollers at the finger tips to help with in-hand reorientation.</p>

      <p>Finally, a reasonable argument against dexterous hands is that even
      humans often do some of their most interesting manipulation not with the
      hand directly, but through tools. I particularly liked the response that
      Matt Mason, one of the main advocates for simple grippers throughout the
      years, gave to
      <a href="https://youtu.be/LfWiBdOc2FI?t=4025">a question at the end of
      one of our robotics seminars</a>: he argued that useful robots in e.g.
      the kitchen will probably have special purpose tools that can be changed
      quickly. In applications where the primary job of the dexterous hand is
      to change tools, we might skip the complexity by mounting a <a
      href="https://blog.robotiq.com/bid/72926/Top-Manufacturers-of-Robotic-Tool-Changers">"tool
      changer"</a>
      directly to the robot and using tool-changer-compatible tools.</p>

    </subsection>

    <subsection><h1>If you haven't seen it...</h1>

      <p>One time I was attending an event where the registration form asked us
      "what is your favorite robot of all time, real or fictional".  That is a
      tough question for someone who loves robots! But the answer I gave was a super cool "high-speed multifingered hand" by
      the <a href="http://ishikawa-vision.org/fusion/index-e.html">Ishikawa group</a>; a project that started turning out
      amazing results back in 2004! They "overclocked" the hand -- sending more current for short durations than would be
      reasonable for any longer applications -- and also used high-speed cameras to achieve these results. And they had a <a
        href="http://ishikawa-vision.org/fusion/RubikManipulation/index-e.html">Rubik's cube demo</a>, too, in 2017.</p>

      <figure>
      <iframe width="560" height="315" src="https://www.youtube.com/embed/-KxjVlaLBmk" frameborder="0"
        allow="accelerometer; encrypted-media; gyroscope; picture-in-picture" allowfullscreen pdf="no"></iframe>
        <p pdf="only"><a href="https://www.youtube.com/embed/-KxjVlaLBmk">Click here to watch the video.</a></p>
      </figure>
      
      <p>So good!</p>

    </subsection>

  </section>

  <todo>Section on mobile manipulators.  PR-2. HSR. Fetch. Everyday robot. TTT.</todo>

  <section><h1>Sensors</h1>
  
    <p>I haven't said much yet about sensors.  In fact, sensors are going to be
    a major topic for us when we get to perception with (depth) cameras, and
    when we think about <a
    href="https://en.wikipedia.org/wiki/Tactile_sensor">tactile sensing</a>. But
    I will defer those topics until we need them.</p>

    <p>For now, let us focus on the joint sensors on the robot.  Both the iiwa and the Schunk WSG provide joint feedback -- the iiwa driver gives "measured position", "estimated velocity", and "measured torque" at each of its seven joints; remember that joint accelerations are typically considered too noisy to rely on.  Similarly the Schunk WSG outputs "measured state" (position + velocity) and "measured force".  We can make all of these available as ports in a block diagram.</p>
  
  </section>
  
  <section><h1>Putting it all together</h1>
  
    <p>If you've worked through the examples, you've seen that a proper
    simulation of our robot is more than just a physics engine -- it requires
    assembling physics, actuator and sensor models, and low-level robot
    controllers into a common framework.  In practice, in Drake, that means that
    we are assembling increasingly sophisticated block diagrams.</p>

    <subsection><h1>HardwareStation</h1>

    <p>One of the best things about the block-diagram modeling paradigm is the
    power of abstraction and encapsulation.  We can assemble a
    <code>Diagram</code> that contains all of the components necessary to
    simulate our hardware platform and its environment, which we will refer to
    affectionately as the "Hardware Station". The method <code>MakeHardwareStation</code> takes a YAML description of the scene and the robot hardware. For a yaml file describing the iiwa + WSG and some cameras, the resulting 
    <code>HardwareStation</code> system looks like this:</p>
    
    <div id="manipulation_station"/> <!-- deprecation shim -->
    <div id="hardware_station">
      <script type="text/javascript">
      var sys = jsyaml.load(`
name: HardwareStation
input_ports:
- iiwa.position
- iiwa.feedforward_torque (optional)
- wsg.position
- wsg.force_limit (optional)
output_ports:
- iiwa.position_commanded
- iiwa.position_measured
- iiwa.velocity_estimated
- iiwa.state_estimated
- iiwa.torque_commanded
- iiwa.torque_measured
- iiwa.torque_external
- wsg.state_measured
- wsg.force_measured
- camera_[NAME].rgb_image
- camera_[NAME].depth_image
- <b style="color:orange">camera_[NAME].label_image</b>
- ...
- camera_[NAME].rgb_image
- camera_[NAME].depth_image
- <b style="color:orange">camera_[NAME].label_image</b>
- <b style="color:orange">query_object</b>
- <b style="color:orange">contact_results</b>
- <b style="color:orange">plant_continuous_state</b>
- <b style="color:orange">body_poses</b>`);
      document.write(system_html(sys, "https://github.com/RussTedrake/manipulation/blob/ceb817b527cbf1826c5b9a573ffbef415cb0f013/manipulation/scenarios.py#L453"));
      </script>
    </div>

    <p>The output ports labeled in in <b><span style="color:orange">orange</span></b> on the diagram above are "cheat ports" -- they are available in simulation, but cannot be available when running on the real robot (because they assume a ground-truth knowledge).</p>

    <example><h1>Hardware station in the teleop demo</h1>

      <p>The teleop notebook in the first chapter used the
        <code>MakeHardwareStation</code> interface to set up the simulation.
        Now you have a better sense for what is going on inside that subsystem!
        Here is the link if you want to take a look at that example again:</p>
  
        <script>document.write(notebook_link('intro', d=deepnote, link_text=""))</script>
  
    </example>

    <example><h1>A bimanual manipulation station</h1>
      
      <p>By adding a few more lines to the YAML file, we can use the same 
      <code>MakeHardwareStation</code> method to construct a bimanual
      station:</p>

      <script>document.write(notebook_link('robot', d=deepnote, link_text="",notebook='bimanual'))</script>

    </example>
    
    <p>If there are other robots/drivers that you'd like to simulate, you can
    make local modifications to the <code>station.py</code> file directly, or
    just ask me and I can probably add them quickly.</p>

    </subsection>
    <subsection><h1>HardwareStationInterface</h1>
    <p>As you see in the examples, the <code>HardwareStation</code> diagram
    itself is intended to be used as a <code>System</code> in additional
    diagrams, which can include our perception, planning, and, higher-level
    control systems.  This model also defines the abstraction between the
    simulation and the real hardware.  By simply passing
    <code>hardware=True</code> into the <code>MakeHardwareStation</code>
    method, we instead construct an almost identical system, the
    <code>HardwareStationInterface</code>.</p>
  
    <div>
      <script type="text/javascript">
      var sys = jsyaml.load(`
name: HardwareStationInterface
input_ports:
- iiwa.position
- iiwa.feedforward_torque
- wsg.position
- wsg.force_limit (optional)
output_ports:
- iiwa.position_commanded
- iiwa.position_measured
- iiwa.velocity_estimated
- iiwa.torque_commanded
- iiwa.torque_measured
- iiwa.torque_external
- wsg.state_measured
- wsg.force_measured
- camera_[NAME].rgb_image
- camera_[NAME].depth_image
- ...
- camera_[NAME].rgb_image
- camera_[NAME].depth_image`);
      document.write(system_html(sys, "https://drake.mit.edu/doxygen_cxx/classdrake_1_1examples_1_1manipulation__station_1_1_manipulation_station_hardware_interface.html"));
      </script>
    </div>    
  
  <p>The <code>HardwareStationInterface</code> is also a diagram,
  but rather than being made up of the simulation components like
  <code>MultibodyPlant</code> and <code>SceneGraph</code>, it is made up of
  systems that perform network message passing to interface with the small
  executables that talk to the individual hardware drivers.  If you dig under
  the covers, you will see that we use <a
  href="https://lcm-proj.github.io/">LCM</a> for this instead of ROS messages,
  primarily because LCM is a lighter-weight dependency for our public
  repository (also because multicast UDP is a better choice that TCP/IP for the
  driver level interface).  But many Drake developers/users use <a
  href="https://github.com/RobotLocomotion/drake-ros">Drake in a ROS/ROS2
  ecosystem</a>.</p>
    
  <p>If you do have your own similar robot hardware available, and want to run
  the hardware interface on your machines, I've started putting together a list
  of drivers and bill of materials <a href="station.html">in the
  appendix</a>.</p>
  </subsection>
  
  <subsection><h1>HardwareStation stand-alone simulation</h1>
  
    <p>Using the <code>HardwareStation</code> workflow, it is easy to
    transition from your development in simulation to running on the real
    robot. One additional tool to support this workflow is the stand-alone
    <code>hardware_sim</code> executable. This python script takes the same
    YAML file as as input (via the command line), and starts up a simulation in
    a separate process that acts just like the real robot hardware should...
    sending and receiving the hardware side of the messages. This can be
    valuable for testing that all of your logic still works with the message
    passing layer adding some delay and non-determinism that we cleverly avoid
    when we use <code>MakeHardwareStation(..., hardware=False)</code> in the
    first stages of our development.</p>
  
    <pre>
    <code class="bash">python3 drake/examples/hardware_sim/hardware_sim.py
    --scenario_file=station.yaml --scenario_name=Name</code>
    </pre>

  </subsection>

</section>
  
<section><h1>More HardwareStation examples</h1>

  <p>I love the projects that students put together for this class. To help
  enable those projects (and your future projects, I hope), I will collect a
  few more examples here of setting up the <code>HardwareStation</code> for
  different hardware configurations. Expect this list to grow over time!</p>

  <example><h1>The iiwa with an Allegro hand</h1>

    <p>Here is a simple example of simulating the iiwa with the Allegro hand
    attached instead of the Schunk WSG gripper. (Note that there are both left
    and right versions of the Allegro hand available.)</p>

    <script>document.write(notebook_link('robot', d=deepnote, link_text="",notebook='iiwa_with_allegro'))</script>

  </example>

  </section>

  <section><h1>Exercises</h1>

    <exercise><h1>Role of Reflected Inertia</h1>

      <p> For this exercise you will investigate the effect of reflected inertia on the joint-space dynamics of the robot, and how it affects simple position control laws. You will work exclusively in <script>document.write(notebook_link('robot', d=deepnote, link_text='this notebook', notebook='01_reflected_inertia'))</script>. You will be asked to complete the following steps: </p>

      <ol type="a">
        <li> Derive the first-order state-space dynamics $\dot{\bx} = f(\bx, \bu)$ of a simple pendulum with a motor and gearbox. 
        </li>
        <li> Compare the behavior of the direct-driven simple pendulum and the simple pendulum with a high-ratio gearbox, under the same position control law.</li>
      </ol>
    </exercise>

    <exercise><h1>Input and Output Ports on the Manipulation Station</h1>

      <p> For this exercise you will investigate how a manipulation station is abstracted in Drake's system-level framework. You will work exclusively in <script>document.write(notebook_link('robot', d=deepnote, link_text='this notebook', notebook='02_hardware_station_io'))</script>. You will be asked to complete the following steps: </p>

      <ol type="a">
        <li> Learn how to probe into inputs and output ports of the manipulation station and evaluate their contents.
        </li>
        <li> Explore what different ports correspond to by probing their values.</li>
      </ol>
    </exercise>    

  </h1></section>

    <exercise><h1>Direct Joint Teleop in Drake</h1>

      <p> For this exercise you will implement a method for controlling the joints of a robot in Drake. You will work exclusively in <script>document.write(notebook_link('robot', d=deepnote, link_text='this notebook', notebook='03_direct_joint_control'))</script>, and should use the <script>document.write(notebook_link('intro', deepnote, link_text='example notebook in chapter 1'))</script> as a reference. You will be asked to complete the following steps: </p>

      <ol type="a">
        <li> Replace the teleop interface in the chapter 1 example with different Drake functions that allow for directly controlling the joints of the robot.</li>
      </ol>
    </exercise>    

  </h1></section>
  
</chapter>
<!-- EVERYTHING BELOW THIS LINE IS OVERWRITTEN BY THE INSTALL SCRIPT -->

<div id="references"><section><h1>References</h1>
<ol>

<li id=Hwangbo19>
<span class="author">Jemin Hwangbo and Joonho Lee and Alexey Dosovitskiy and Dario Bellicoso and Vassilios Tsounis and Vladlen Koltun and Marco Hutter</span>, 
<span class="title">"Learning agile and dynamic motor skills for legged robots"</span>, 
<span class="publisher">Science Robotics</span>, vol. 4, no. 26, pp. eaau5872, <span class="year">2019</span>.

</li><br>
<li id=Asada87>
<span class="author">Haruhiko Asada and Kamal Youcef-Toumi</span>, 
<span class="title">"Direct-Drive Robots - Theory and Practice"</span>, The MIT Press
, <span class="year">1987</span>.

</li><br>
<li id=Wensing17>
<span class="author">P. M. Wensing and A. {Wang} and S. {Seok} and D. {Otten} and J. {Lang} and S. {Kim}</span>, 
<span class="title">"Proprioceptive Actuator Design in the MIT Cheetah: Impact Mitigation and High-Bandwidth Physical Interaction for Dynamic Legged Robots"</span>, 
<span class="publisher">IEEE Transactions on Robotics</span>, vol. 33, no. 3, pp. 509-522, June, <span class="year">2017</span>.

</li><br>
<li id=Kashiri17>
<span class="author">Navvab Kashiri and Jörn Malzahn and Nikos Tsagarakis</span>, 
<span class="title">"On the Sensor Design of Torque Controlled Actuators: A Comparison Study of Strain Gauge and Encoder Based Principles"</span>, 
<span class="publisher">IEEE Robotics and Automation Letters</span>, vol. PP, 02, <span class="year">2017</span>.

</li><br>
<li id=Wedler12>
<span class="author">A Wedler and M Chalon and K Landzettel and M G{\"o}rner and E Kr{\"a}mer and R Gruber and A Beyer and HJ Sedlmayr and B Willberg and W Bertleff and others</span>, 
<span class="title">"DLRs dynamic actuator modules for robotic space applications"</span>, 
<span class="publisher">Proceedings of the 41st Aerospace Mechanisms Symposium</span> , May 16-18, <span class="year">2012</span>.

</li><br>
<li id=Pratt95b>
<span class="author">G. A. Pratt and M. M. {Williamson}</span>, 
<span class="title">"Series elastic actuators"</span>, 
<span class="publisher">Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots</span> , vol. 1, pp. 399-406 vol.1, Aug, <span class="year">1995</span>.

</li><br>
<li id=Albu-Schaffer07>
<span class="author">Alin Albu-Schaffer and Christian Ott and Gerd Hirzinger</span>, 
<span class="title">"A unified passivity-based control framework for position, torque and impedance control of flexible joint robots"</span>, 
<span class="publisher">The international journal of robotics research</span>, vol. 26, no. 1, pp. 23--39, <span class="year">2007</span>.

</li><br>
<li id=Pang18>
<span class="author">Tao Pang and Russ Tedrake</span>, 
<span class="title">"A Robust Time-Stepping Scheme for Quasistatic Rigid Multibody Systems"</span>, 
<span class="publisher">IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)</span> , <span class="year">2018</span>.
[&nbsp;<a href="http://groups.csail.mit.edu/robotics-center/public_papers/Pang18.pdf">link</a>&nbsp;]

</li><br>
<li id=Kim19>
<span class="author">Yong-Jae Kim and Junsuk Yoon and Young-Woo Sim</span>, 
<span class="title">"Fluid Lubricated Dexterous Finger Mechanism for Human-Like Impact Absorbing Capability"</span>, 
<span class="publisher">IEEE Robotics and Automation Letters</span>, vol. 4, no. 4, pp. 3971--3978, <span class="year">2019</span>.

</li><br>
<li id=Odhner14>
<span class="author">Lael U. Odhner and Leif P. Jentoft and Mark R. Claffee and Nicholas Corson and Yaroslav Tenzer and Raymond R. Ma and Martin Buehler and Robert Kohout and Robert D. Howe and Aaron M. Dollar</span>, 
<span class="title">"A Compliant, Underactuated Hand for Robust Manipulation"</span>, 
<span class="publisher">International Journal of Robotics Research (IJRR)</span>, vol. 33, no. 5, pp. 736-752, <span class="year">2014</span>.

</li><br>
<li id=Brown10>
<span class="author">Eric Brown and Nicholas Rodenberg and John Amend and Annan Mozeika and Erik Steltz and Mitchell R Zakin and Hod Lipson and Heinrich M Jaeger</span>, 
<span class="title">"Universal robotic gripper based on the jamming of granular material"</span>, 
<span class="publisher">Proceedings of the National Academy of Sciences</span>, vol. 107, no. 44, pp. 18809–18814, <span class="year">2010</span>.

</li><br>
</ol>
</section><p/>
</div>

<table style="width:100%;" pdf="no"><tr style="width:100%">
  <td style="width:33%;text-align:left;"><a class="previous_chapter" href=intro.html>Previous Chapter</a></td>
  <td style="width:33%;text-align:center;"><a href=index.html>Table of contents</a></td>
  <td style="width:33%;text-align:right;"><a class="next_chapter" href=pick.html>Next Chapter</a></td>
</tr></table>

<div id="footer" pdf="no">
  <hr>
  <table style="width:100%;">
    <tr><td><a href="https://accessibility.mit.edu/">Accessibility</a></td><td style="text-align:right">&copy; Russ
      Tedrake, 2023</td></tr>
  </table>
</div>


</body>
</html>
